As for places to see i suggest you rent a Suzuki for one day at least and have a scout around the island, check out Wat Chalong, Cape Panwa, there's a great viewpoint up on the cliffs past Kata, also have a look around Phuket town, there's some nice old-style architecture to see. As for shopping have a look in Tesco Lotus and compare prices there before buying too much from the street stalls. Also there are daytrips/overnight trips you can make from phuket, probably the most popular are to PP Islands, and James Bond Is. Worth looking into.